It doesn't matter and if you have them separate, they can be combined later on. My parents started 2 for my 2 kids. We have since had them combine them so we could use the money sooner for our first son. Beneficiary on the other son's 529 was changed, then the 2 were combined.

Either way can work fine. I have two because I have twins who were born with amazing "fairness" sensors. That is, they very much pay attention to what the other is being given. I decided to avoid any conflict between them re college funding by opening two accounts which I fund identically.

What is the age difference ?
If my kids were more then 4 years apart, definitely one account.
Once first graduates, you can simply change the beneficiary.
The only advantage to separate them in this case, is if you use target date funds and the age different is large enough
to have 2 funds with different targets, but then again, you can own both funds in same account potentially.
If you consider 2 target funds in same acct, ask your plan admin if that is possible.

Mine were 2 years apart, and have to pay 2 schools. Hence I have 2 accounts,
But could have easily left all in one account until the 2nd kid finished HS.
Already transferred from one kid to the other when money was due and one kid has a smaller balance.
Was easy to do.

Is there any benefit to actually starting a second separate 529 or is it better to just start contributing double the amount to the 529 already in place?

Since the 529s are transferrable to siblings it seems option 2 would be ok. Curious how others have tackled this?

The asset allocation for one can be much different than that of the second child. Consider this, most folks will gradually make the allocation more conservative as college looms to preserve the value of the amounts accumulated and have the monies available for spending. A younger child has the benefit of time, allowing one to invest more aggressively. A very young child could be invested at 80/20 or higher, a 17 year old child may want to be 30/70 or 50./50 or even more conservative to ensure monies are available to pay the first tuition bill. Not everyone has the luxury of holding a high equity allocation come school time, this forum is the apparent exception.

Depending on your state and whether you get a tax break, it may be a good idea to open more than one, even if you only have one kid. For example, in Virginia, you can deduct up to $4,000 saved per child per account, so if you are saving a lot per child, you can open multiple accounts and increase your state tax deduction. For example, I have four accounts for each of my children, so I could, in theory, get a $32,000 deduction on my state taxes every year.

Another advantage is that you can invest in different funds that may be cost less than a single "age-based" fund, give you more flexibility, or allow you to vary the risk of each portfolio.

If you will have both kids in school at the same time, two accounts will also allow you to fund their education simultaneously.

I would highly recommend separate accounts. You can only use account for beneficiary. Since both will likely be in college with some overlapping years, you will need separate accounts at that time anyway. Once the oldest is done, you can combine if any $ leftover from the first.

Once in a while you get shown the light, in the strangest of places if you look at it right.